The consequences of imposing such a constraint leads to a functional equation (see e.g., [1]}) whose general solution was first found by Cox (see e.g., [2]}[3]}). Unfortunately, for an arbitrary ranking scheme \([\, \cdot \, ]\) , the general solution is quite complicated. Cox, however, demonstrated that one could always regraduate (or rescale) the degrees of belief
\([\, \cdot \, ]\rightarrow \xi (\cdot ),\) 
